Group averaging for de Sitter free fields in terms of hyperspherical functions

TL;DR

This paper investigates the convergence of inner products for free fields in de Sitter space using hyperspherical functions, providing detailed calculations for two-particle states on a four-dimensional hyperboloid.

Contribution

It introduces a method to analyze the convergence of inner products in de Sitter space via hypergeometric functions, with explicit calculations for two-particle states.

Findings

Convergence depends on hypergeometric function asymptotics.

Inner product calculations are explicitly performed for two-particle states.

Provides insights into the structure of free fields in de Sitter space.

Abstract

We study the convergence of inner products of free fields over the homogeneous spaces of the de Sitter group and show that the convergence of inner products in the of $N$-particle states is defined by the asymptotic behavior of hypergeometric functions. We calculate the inner product for two-particle states on the four-dimensional hyperboloid in detail.